In discriminant analysis, the dependent variable is categorical, but can I use a categorical variable (e.g residential status: rural, urban) along with some other continuous variable as independent variable in linear discriminant analysis?
Discriminant analysis assumes a multivariate normal distribution because what we usually consider to be predictors are really a multivariate dependent variable, and the grouping variable is considered to be a predictor. This means that categorical variables that are to be treated as predictors in the sense you wish are not handled well. This is one reason that many, including myself, consider discriminant analysis to have been made obsolete by logistic regression. Logistic regression makes no distributional assumptions of any kind, on either the left hand or the right hand side of the model. Logistic regression is a direct probability model and doesn’t require one to use Bayes’ rule to convert results to probabilities as does discriminant analysis.